1. The problem statement, all variables and given/known data I have this theorem which I am having trouble understanding due to notation. Theorem: Define S,S'[itex]\subseteq[/itex]ℝ3 to be surfaces. Let f:S→S' be a smooth map. f is a local isometry if for all p in S, and all w1,w2 in TpS, <w1,w2>=<dfp(w1),dfp(w2)>. The thing I don't get, is what does dfp(w1) mean? What action is going on between dfp and w1? Thank you for your time.